Models consider
##
## Calls:
## m01AIC: lm(formula = log(df_sub$ARPU + 1) ~ Brand.total + DiD, data = df_sub)
## m02AIC: lm(formula = df_sub$ARPU ~ Brand.total + Stables.total + DiD,
## data = df_sub)
## m10: lm(formula = I(log(ARPU + 1)) ~ spread_moex + USDT + Ставка +
## time_period + time_period + Group + DiD, data = df)
## m11: lm(formula = I(log(ARPU + 1)) ~ spread_moex + USDT + Ставка +
## time_period + I(Brand.total) + I(Stables.total) + time_period +
## Group + DiD, data = df)
## m12: lm(formula = I(log(ARPU + 1)) ~ spread_moex + USDT + Ставка +
## time_period + I(log(Brand.total)) + I(log(Stables.total)) +
## time_period + Group + DiD, data = df)
## m13: lm(formula = ARPU ~ spread_moex + USDT + Ставка + time_period +
## I(log(Brand.total)) + I(log(Stables.total)) + time_period +
## Group + DiD, data = df)
##
## ===============================================================================================================================
## m01AIC m02AIC m10 m11 m12 m13
## --------------------- ------------ ----------------- ----------------- ----------------- ------------
## log(df_sub$ARPU + 1) df_sub$ARPU I(log(ARPU + 1)) I(log(ARPU + 1)) I(log(ARPU + 1)) ARPU
## -------------------------------------------------------------------------------------------------------------------------------
## (Intercept) 5.873*** 884.138 10.893 10.020 9.759 29669.910
## (0.495) (2082.288) (6.499) (6.353) (12.706) (35423.912)
## Brand.total 0.000** 0.438*
## (0.000) (0.186)
## DiD 0.511* 1682.661** 0.759 0.759 0.759 1599.458
## (0.184) (540.337) (0.443) (0.414) (0.411) (1146.297)
## Stables.total -0.051
## (0.036)
## spread_moex 0.062 0.142 0.143 511.151
## (0.203) (0.211) (0.205) (570.598)
## USDT 0.031 -0.009 -0.004 -6.429
## (0.091) (0.087) (0.086) (239.143)
## Ставка -0.006 -0.004 -0.004 -10.572
## (0.004) (0.005) (0.005) (12.623)
## time_period -1.144 -0.293 -0.311 -69.666
## (0.606) (0.692) (0.674) (1880.255)
## Group -0.262 -0.262 -0.262 -116.372
## (0.369) (0.345) (0.342) (953.777)
## I(Brand.total) 0.000
## (0.000)
## I(Stables.total) -0.000
## (0.000)
## I(log(Brand.total)) 1.544* 3753.891
## (0.708) (1974.495)
## I(log(Stables.total)) -1.225 -5116.024
## (0.972) (2709.694)
## -------------------------------------------------------------------------------------------------------------------------------
## AIC 36.647 450.425 47.797 45.396 44.983 457.502
## BIC 41.680 456.716 57.862 57.977 57.564 470.083
## adj. R-squared 0.354 0.306 0.118 0.229 0.241 0.198
## N 26 26 26 26 26 26
## ===============================================================================================================================
## Significance: *** = p < 0.001; ** = p < 0.01; * = p < 0.05
Check normality assumption
## Warning: Ignoring unknown parameters: main
## [[1]]
## [1] "m01AIC"
##
##
## Jarque-Bera Normality Test
##
## data: as.vector(m1$residuals)
## JB = 2.0464, p-value = 0.3594
## alternative hypothesis: greater
##
## lag Autocorrelation D-W Statistic p-value
## 1 -0.1342492 2.21838 0.648
## Alternative hypothesis: rho != 0
##
## RESET test
##
## data: m1
## RESET = 0.093995, df1 = 1, df2 = 22, p-value = 0.762
##
## [1] "======================================"
## Warning: Ignoring unknown parameters: main
## [[1]]
## [1] "m02AIC"
##
##
## Jarque-Bera Normality Test
##
## data: as.vector(m1$residuals)
## JB = 29.119, p-value = 4.751e-07
## alternative hypothesis: greater
##
## lag Autocorrelation D-W Statistic p-value
## 1 -0.1751643 2.264155 0.664
## Alternative hypothesis: rho != 0
##
## RESET test
##
## data: m1
## RESET = 0.48333, df1 = 1, df2 = 21, p-value = 0.4945
##
## [1] "======================================"
## Warning: Ignoring unknown parameters: main
## Warning: Computation failed in `stat_bin()`:
## attempt to apply non-function
## [[1]]
## [1] "m10"
##
##
## Jarque-Bera Normality Test
##
## data: as.vector(m1$residuals)
## JB = 0.11476, p-value = 0.9442
## alternative hypothesis: greater
##
## lag Autocorrelation D-W Statistic p-value
## 1 0.1867099 1.548469 0.138
## Alternative hypothesis: rho != 0
##
## RESET test
##
## data: m1
## RESET = 0.84365, df1 = 1, df2 = 18, p-value = 0.3705
##
## [1] "======================================"
## Warning: Ignoring unknown parameters: main
## Warning: Computation failed in `stat_bin()`:
## attempt to apply non-function
## [[1]]
## [1] "m11"
##
##
## Jarque-Bera Normality Test
##
## data: as.vector(m1$residuals)
## JB = 0.060428, p-value = 0.9702
## alternative hypothesis: greater
##
## lag Autocorrelation D-W Statistic p-value
## 1 -0.1474577 2.222687 0.946
## Alternative hypothesis: rho != 0
##
## RESET test
##
## data: m1
## RESET = 0.078645, df1 = 1, df2 = 16, p-value = 0.7827
##
## [1] "======================================"
## Warning: Ignoring unknown parameters: main
## Warning: Computation failed in `stat_bin()`:
## attempt to apply non-function
## [[1]]
## [1] "m12"
##
##
## Jarque-Bera Normality Test
##
## data: as.vector(m1$residuals)
## JB = 0.058093, p-value = 0.9714
## alternative hypothesis: greater
##
## lag Autocorrelation D-W Statistic p-value
## 1 -0.1559159 2.239441 0.928
## Alternative hypothesis: rho != 0
##
## RESET test
##
## data: m1
## RESET = 0.19566, df1 = 1, df2 = 16, p-value = 0.6642
##
## [1] "======================================"
## Warning: Ignoring unknown parameters: main
## [[1]]
## [1] "m13"
##
##
## Jarque-Bera Normality Test
##
## data: as.vector(m1$residuals)
## JB = 12.402, p-value = 0.002027
## alternative hypothesis: greater
##
## lag Autocorrelation D-W Statistic p-value
## 1 -0.2894041 2.489903 0.532
## Alternative hypothesis: rho != 0
##
## RESET test
##
## data: m1
## RESET = 4.2922, df1 = 1, df2 = 16, p-value = 0.05481
##
## [1] "======================================"
Autocorrelation
j = 1
for (i in names_m_i) {
m1 = i
ts4 = zoo(studres((m1)))#, order.by=time(df1))
ts4_lag = lag(ts4, k = -1)[c(-dim(m1$model)[1] )]
ts4_lag
df_res = data.frame(ts4[c(-1)], ts4_lag)
df_res
plot(df_res$ts4.c..1.., df_res$ts4_lag , col = 'blue3', pch = 20, main = names_m[j])
abline(h = median(studres((m1))), col = 'red2')
abline(v = median(studres((m1))), col = 'red2')
df_res_t = data.frame(df$time, studres(m1))
print(ggplot(df_res_t, aes(x = df_res_t[, 1], y=df_res_t[, 2]))+geom_line(col = "blue3", alpha = 0.85, size = 0.8)+ylab(colnames(df_res_t)[2])+xlab(names_m[j])+geom_point(size = 3))
print("corr coef: ")
print(cor(df_res$ts4.c..1.., df_res$ts4_lag))
j = j + 1
}
## [1] "corr coef: "
## [1] -0.1276279
## [1] "corr coef: "
## [1] -0.151565
## [1] "corr coef: "
## [1] 0.1432378
## [1] "corr coef: "
## [1] -0.1768364
## [1] "corr coef: "
## [1] -0.1833807
## [1] "corr coef: "
## [1] -0.2785566
datatable(vcovHAC(m11))
acf(m11$residuals, type = "correlation")
Heteroscedasticity
Goldfeld-Quandt test
## [[1]]
## [1] "m01AIC"
##
##
## Goldfeld-Quandt test
##
## data: m1
## GQ = 0.83892, df1 = 8, df2 = 7, p-value = 0.5983
## alternative hypothesis: variance increases from segment 1 to 2
##
## [[1]]
## [1] "m02AIC"
##
##
## Goldfeld-Quandt test
##
## data: m1
## GQ = 2.1326, df1 = 7, df2 = 6, p-value = 0.1875
## alternative hypothesis: variance increases from segment 1 to 2
##
## [[1]]
## [1] "m10"
##
##
## Goldfeld-Quandt test
##
## data: m1
## GQ = 2.733, df1 = 4, df2 = 3, p-value = 0.2175
## alternative hypothesis: variance increases from segment 1 to 2
##
## [[1]]
## [1] "m11"
##
##
## Goldfeld-Quandt test
##
## data: m1
## GQ = 0.88623, df1 = 2, df2 = 1, p-value = 0.6006
## alternative hypothesis: variance increases from segment 1 to 2
##
## [[1]]
## [1] "m12"
##
##
## Goldfeld-Quandt test
##
## data: m1
## GQ = 0.88623, df1 = 2, df2 = 1, p-value = 0.6006
## alternative hypothesis: variance increases from segment 1 to 2
##
## [[1]]
## [1] "m13"
##
##
## Goldfeld-Quandt test
##
## data: m1
## GQ = 0.72595, df1 = 2, df2 = 1, p-value = 0.6386
## alternative hypothesis: variance increases from segment 1 to 2
Multicollinearity
Condition number, VIF
##
## Call:
## lm(formula = log(df_sub$ARPU + 1) ~ Brand.total + DiD, data = df_sub)
##
## Coefficients:
## (Intercept) Brand.total DiD
## 5.8727770 0.0001955 0.5106329
##
## [1] "CN: "
## [1] 16780.49
## [1] "VIF: "
## Brand.total DiD
## 1.003267 1.003267
## [1] "==========================="
##
## Call:
## lm(formula = df_sub$ARPU ~ Brand.total + Stables.total + DiD,
## data = df_sub)
##
## Coefficients:
## (Intercept) Brand.total Stables.total DiD
## 884.13842 0.43848 -0.05091 1682.66076
##
## [1] "CN: "
## [1] 135118.7
## [1] "VIF: "
## Brand.total Stables.total DiD
## 1.027484 1.107771 1.092117
## [1] "==========================="
##
## Call:
## lm(formula = I(log(ARPU + 1)) ~ spread_moex + USDT + Ставка +
## time_period + time_period + Group + DiD, data = df)
##
## Coefficients:
## (Intercept) spread_moex USDT Ставка time_period Group
## 10.893212 0.062414 0.030834 -0.006337 -1.144205 -0.261930
## DiD
## 0.759081
##
## [1] "CN: "
## [1] 5683.098
## [1] "VIF: "
## spread_moex USDT Ставка time_period Group DiD
## 4.630041 1.441197 12.401259 7.470051 3.250000 4.250000
## [1] "==========================="
##
## Call:
## lm(formula = I(log(ARPU + 1)) ~ spread_moex + USDT + Ставка +
## time_period + I(Brand.total) + I(Stables.total) + time_period +
## Group + DiD, data = df)
##
## Coefficients:
## (Intercept) spread_moex USDT Ставка
## 1.002e+01 1.423e-01 -8.908e-03 -3.839e-03
## time_period I(Brand.total) I(Stables.total) Group
## -2.935e-01 1.963e-04 -2.102e-05 -2.619e-01
## DiD
## 7.591e-01
##
## [1] "CN: "
## [1] 383606.1
## [1] "VIF: "
## spread_moex USDT Ставка time_period
## 5.702496 1.514602 16.536084 11.139683
## I(Brand.total) I(Stables.total) Group DiD
## 1.716091 1.968835 3.250000 4.250000
## [1] "==========================="
##
## Call:
## lm(formula = I(log(ARPU + 1)) ~ spread_moex + USDT + Ставка +
## time_period + I(log(Brand.total)) + I(log(Stables.total)) +
## time_period + Group + DiD, data = df)
##
## Coefficients:
## (Intercept) spread_moex USDT
## 9.758794 0.142780 -0.003689
## Ставка time_period I(log(Brand.total))
## -0.004029 -0.310692 1.544391
## I(log(Stables.total)) Group DiD
## -1.224944 -0.261930 0.759081
##
## [1] "CN: "
## [1] 9095.894
## [1] "VIF: "
## spread_moex USDT Ставка
## 5.468535 1.492173 15.765233
## time_period I(log(Brand.total)) I(log(Stables.total))
## 10.762144 1.668016 2.004922
## Group DiD
## 3.250000 4.250000
## [1] "==========================="
##
## Call:
## lm(formula = ARPU ~ spread_moex + USDT + Ставка + time_period +
## I(log(Brand.total)) + I(log(Stables.total)) + time_period +
## Group + DiD, data = df)
##
## Coefficients:
## (Intercept) spread_moex USDT
## 29669.910 511.151 -6.429
## Ставка time_period I(log(Brand.total))
## -10.572 -69.666 3753.891
## I(log(Stables.total)) Group DiD
## -5116.024 -116.372 1599.458
##
## [1] "CN: "
## [1] 30639.87
## [1] "VIF: "
## spread_moex USDT Ставка
## 5.468535 1.492173 15.765233
## time_period I(log(Brand.total)) I(log(Stables.total))
## 10.762144 1.668016 2.004922
## Group DiD
## 3.250000 4.250000
## [1] "==========================="
Significance of coefficients with HAC correction for m01AIC
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.8728e+00 3.9597e-01 14.8314 2.899e-13 ***
## Brand.total 1.9550e-04 5.3126e-05 3.6799 0.001241 **
## DiD 5.1063e-01 2.1418e-01 2.3841 0.025756 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
